We consider the problem of path inference: given a path prefix, i.e., a partially observed sequence of nodes in a graph, we want to predict which nodes are in the missing suffix. In particular, we focus on natural paths occurring as a by-product of the interaction of an agent with a network---a driver on the transportation network, an information seeker in Wikipedia, or a client in an online shop. Our interest is sparked by the realization that, in contrast to shortest-path problems, natural paths are usually not optimal in any graph-theoretic sense, but might still follow predictable patterns. Our main contribution is a graph neural network called Gretel. Conditioned on a path prefix, this network can efficiently extrapolate path suffixes, evaluate path likelihood, and sample from the future path distribution. Our experiments with GPS traces on a road network and user-navigation paths in Wikipedia confirm that Gretel is able to adapt to graphs with very different properties, while also comparing favorably to previous solutions.